The minimizing of clearances, especially the radial clearances between stationary and rotating parts of a turbomachine during operation is vital for minimizing flow losses and therefore for maximizing the efficiency of such machines. By way of illustration, FIG. 1 shows an example of a turbomachine 10 in the form of a compressor arrangement with a rotor blade 14 which is seated on a rotating (around an axis 13) shaft 12 and a stator blade 15 which is fastened on a casing 11. By minimizing the radial clearances Cb and Cv between the tips of the rotor blade 14 and the oppositely disposed casing 11 or between the tip of the stator blade 15 and the oppositely disposed shaft 12, the flow losses can be reduced.
On account of the relative movement, e.g. between the blade tip of the rotor blade 14 and the casing 11, it is not possible to set the radial clearance to zero. Contact between both parts during operation can lead to damage or even to the complete destruction of the parts.
It is basically the case that the radial clearances during operation (so-called “hot clearances”) are determined by a series of factors which have to be taken into consideration in the construction of such a machine when the assembly clearances (so-called “cold clearances”, in the stationary state of the cold machine) are determined                The manufacturing tolerances of the individual components;        The assembly tolerances;        The expansion of the blades during operation on account of thermal effects and centrifugal forces;        The deformation of shaft and casing in steady-state operation (e.g. in the form of so-called “ovalization”) and        Time-dependent deformations and relative movements of all components during transient machine operation (operational transition phase of the machine), such as the starting up or the shutting down of the machine.        
In particular, the time-dependent deformations and relative movements of the main components during transient operation are of importance for the determination of the cold clearance and the hot clearance resulting therefrom. The aim is to determine the cold clearance in such a way that during steady-state operation the resulting hot clearance is minimal. On account of the different time constants in the mechanical and thermal deformation of the blades, of the casing parts and of the shafts during the warming-up or cooling-down of the machine, the minimum hot clearance will not necessarily occur during hot steady-state operation where the minimum clearance is desired. As a rule, the smallest possible clearance (so-called “pinch point”) will occur during a transient operating phase, especially if it is taken into consideration that the machine is also subjected to rapid load changes or can be started when essential components are still hot from a previous operating period. In such a case, it is necessary to increase the cold clearance to such an extent that a hard contact between stationary and rotating parts during the transient operation is avoided, which then consequentially leads under steady-state conditions to a hot clearance which is larger than desired.
Measures for minimizing the flow losses, which are created as a result of remaining hot clearances, include, for example, the introduction of shrouds at the tips of the rotor blade airfoils and stator blade airfoils. In order to minimize the flow through the annular gap between shroud and casing or rotor, a rib, or a plurality of ribs, are frequently provided on the rotating part in the circumferential direction, whereas the surface of the stationary part can be flat or stepped in order to collectively form a labyrinth-like seal. Furthermore, so-called honeycombs (honeycomb-like material) can be arranged on the surface of the stationary part in order to enable the ribs to cut in during the transient operating states so as to avoid a hard contact. The configuration consisting of rotating part and cut-in honeycomb, which results in the process, resembles a stepped labyrinth seal and helps to reduce the flow losses compared with a configuration without honeycomb. Further measures for minimizing the hot clearances entail attaching so-called leaf seals or brush seals on the stationary part which can compensate the changes in the clearance during operating transition phases up to a certain degree.
Finally, a combination of abrading elements and abradable coatings, for example, can be used on the counter side in order to alleviate the negative effect of the clearance variations which occur over the circumference and can be brought about, for example, as a result of the ovalization of structural parts or of a certain eccentricity of the shaft inside the casing.
Whereas all previously mentioned solutions are of a purely passive nature, which enable a minimizing of the hot clearance without any active adjustment of the geometry during operation, there are also a number of active measures for clearance reduction.
Thus, in a system the entire rotor is displaced in the axial direction if the machine has achieved its steady-state operating condition. In conjunction with a conical flow passage, this makes it possible to actively minimize the radial clearances in the hot turbine, wherein a combination with the above-described passive measures is basically possible. Since, however, the entire rotor has to be moved, enlargements of the radial clearances on the compressor side are created. Therefore, this measure is only of advantage providing the reduction of the losses in the turbine outweigh the additional loss on the compressor side.
Instead of a displacement of the shaft, other solutions propose to control either the radial thermal expansion of the blades in each turbine stage, or to use a spring system which enables an additional radial movement of the heat shields above a predetermined limiting temperature.
Adjusting means can be used for the linear adjustment of the clearance or even elastically resilient bearing means can be used. The latter is described in EP 1 467 066 A2, for example. With these technical solutions, it is not possible, however, to compensate an extreme value in the clearance in an operational transition phase of the machine.
Document US 2009/0226327 A1 describes a restrictor, produced from a so-called memory alloy, which is installed in the rotor disk. Depending upon the local temperatures, this restrictor controls the volume of cooling medium flow into the turbine blade. By reducing the cooling medium flow, the blade thermally expands and so reduces the radial gap between the blade tip and the oppositely disposed stationary component. By increasing the cooling medium flow, the blade length is reduced and so increases the radial gap.
Printed publication GB 2 354 290 describes a valve, produced from a memory alloy, which is installed in the cooling passage of the gas turbine blade. The valve regulates the consumption of cooling medium as a function of the temperature of the component. Controlling of the radial clearance for rotor blades and stator blades is not described in this document.
Printed publication U.S. Pat. No. 7,686,569 describes a system for the axial movement of a blade ring which is brought about as a result of a pressure difference applied to the blade ring, of the thermal expansion or contraction of a connection or by a piston. A memory alloy can also bring about the necessary movement.
Different passive, semi-active or active systems, and also combinations thereof, can basically be considered for controlling the clearances between rotating components and stationary components. The clearances Cb or Cv, which define the relative distance between a rotating component and a stationary component (FIG. 1), vary during transient operating states as a consequence of the different and time-dependent thermal and mechanical deformations of the components. The actual time variation depends upon a large number of factors, such as the volume of the components, the contact with hot or cold media, and the thermal properties of the alloys which are used.
On account of these time-differentiated deformations, according to FIG. 2(a) the “hot” clearance Cb (in the case of rotor blades) or Cv (in the case of stator blades), in addition to a safety clearance Cs, must also include a transient portion gt,min. This transient portion must also be taken into consideration in the definition of the clearances in the cold assembled state, Cβ,o,min and Cβ,o,max.
FIG. 2 shows in sub-FIG. 2(a) an example of the change over time t of the clearance between rotating and stationary hot parts for steady-state operating phases (st) and transient operating phases (tr), wherein—as already mentioned—Cs represents a safety clearance, ga is a tolerance band on account of the manufacturing and assembly tolerances of the components, gt,min and gt,max represent the minimum and maximum differences between the clearance in the steady-state condition and the minimum clearance, Cβ,min and Cβ,max stand for the minimum and maximum clearances for the nominal (“hot”) operating conditions, and Cβ,o,min and Cβ,o,max represent the corresponding minimum and maximum clearances in the stationary state (“cold” operating condition) (the index 13 in this case stands for “b” or rotor blade, or “v” or stator blade, see FIG. 1).
FIGS. 2(b) and (c) show possible variations of the rotational speed Ω of the shaft 12, of the temperature T of the working medium (hot gas) and of the metal temperature Tm over time t, wherein Ωn and Tn correspondingly stand for the nominal rotational speed and nominal hot gas temperature in the machine. The metal temperature Tmn refers to the nominal temperature of the shaft and/or to another mechanical component during the steady-state operation of the machine. tΩn and tTn in this case are the time points at which the steady-state values Ωn and Tn are achieved.
FIG. 3 shows the cross section through a rotating component (a rotor blade 14 in the example)—which is fastened by a root 16 in a corresponding carrier in the rotor (shaft 12)—in the stationary state of the machine (FIG. 3(a)) and under nominal steady-state operating conditions (FIG. 3(b)). The depicted root 16 is representative in this case for any root geometry, such as a firtree root, a dovetail root or an inverted-T root. It engages by fingers 18 in corresponding lateral grooves 17 in the carrier, e.g. in the rotor.
The centrifugal force brings one, or a plurality of fingers 18, of the root 16 into contact with the rotor 12 (FIG. 3(b)). At low rotational speed, a spring element 19 prevents the root 16 rattling in the carrier at slow rotational speeds. At nominal rotational speed and after achieving the thermal equilibrium of all the components of the machine, clearances Cb or Cv are achieved according to FIG. 1. The designation ga in this case again stands for the tolerance band consisting of manufacturing and assembly tolerances and is shown here by way of example between fingers 18 and the carrier in the rotor in the stationary state of the machine.
During start-up of the machine, the thermal expansion of the blading is typically very much quicker than that of the casing parts or that of the rotor shaft, which on account of their greater mass have a higher thermal inertia than the blades. This means that the heating up and therefore the thermal expansion of the shaft or other structural parts continues, even after the working medium has already reached the nominal operating temperature Tn (time point tTn in FIG. 2(c)). This circumstance leads to the occurrence of a so-called “pinch point”, i.e. a time point during the warming-up phase during which the radial clearance achieves its minimum value (see FIG. 2(a)). For this reason, for the nominal steady-state operating condition the resulting minimum clearance Cb,min (or Cv,min) must include a safety clearance Cs and also a minimum transient contribution to the clearance gt,min. This must be analytically determined in the design of the machine and depends upon the thermal boundary conditions, dimensions and material properties of the rotating and stationary components. The transient contributions to the gap gt,min and gt,max prevent the blade tips rubbing against the stationary casing or stationary heat shields or against the rotor or the rotor heat shields.
Under the nominal stationary operating condition, if all the rotating and stationary parts have reached their maximum thermal and mechanical deformations, the transient contribution to the “pinch-point” gap (gt) is an essential part of the clearance in the “hot” steady-state condition Cb,min (or Cv,min).